Holographic Superconducting Phase Transition In Modified Gravities

Anti de-Sitter/Conformal Field Theory(AdS/CFT)duality was developed from super-string theory,which describes the duality between strongly coupling sectors and weakly coupling sector.Especially,it connects the low-dimensional gauge field theory and high-dimensional gravity theory.The applications of AdS/CFT duality have great significance on the study of high temperature superconductivity in condensed matter physics.In this thesis,in the first part we try to study the holographic superconducting phase transition in a modified gravity theory with a special non-linear electromagnetic filed,but we do not find a superconducting solution in the probe limit of this theory.We then analyze the quasi-normal mode(QNM)frequencies of the massless neutral scalar field perturbation in Coulomb-like BTZ black hole in the theory,and it is found that the black hole is stable under the perturbation.Besides,recently one of the popular studies on modifying the gravity theory is to introduce the coupling between the scalar field and the Gauss-Bonnet(GB)invariant.Thus,the second part of this thesis is to study the various states of holographic superconductors in such Einstein-scalar-Gauss-Bonnet gravity theory coupled with a scalar field and GB invariants.In addition,we also study the effect of the coupling on the condensation properties of the first three states of holographic superconductors.It shows that the holographic superconducting phase transition will only occur when the coupling parameter is less than the critical value since too strong coupling will force the scalar field to fall into the black hole;also,the coupling strength has significant effects on the critical temperatures of the ground state,the first and second excited states,the condensed strength and the optical conductivity of the superconducting state.The thesis is organized as follows.In the first chapter,we briefly introduce the holographic superconductivity of black holes and its development,then we explain the physical significance of the application of AdS/CFT duality on the study of high-temperature superconductivity.In the second chapter,we introduce some properties of black hole in a gravity theory with a specific non-linear electromagnetic field.By directly solving the equation of motion for matter fields and the study of QNM for the scalar field perturbation,we fail to find the hairy solution in this theory.In the third chapter,focusing on the probe limit in Einstein-scalar-Gauss-Bonnet gravity,we study the critical temperatures,condensation and optical conductivities in the ground state and excited states holographic superconductor with the use of shooting method.The last chapter is our conclusion.